Name: Show Your Work - Final Exam This portion of your Final Exam counts as half of your final exam grade, 50 points. Show all applicable work for each of the following problems. A T184 graphing calculator is allowed for computations - please explain any calculations done with the calculator in order to explain / show your work for each part of this assignment. You will be earning points for each step in the process - not just the correct final answer. You will complete work shown on your own. You may not receive outside assistance on this assignment. Any other questions - ask your instructor via Canvas Messages. Linear Regression (11 points) In an area of the Midwest, records were kept on the relationship between the rainfall (in inches) and the yield of wheat (bushels per acre). Below is the data: (Round to four decimal places). Rain fall 10.8 8.9 13.2 12.5 18.8 10.9 7.0 15.6 16.0 (in inches), X Yield 51.5 46.0 56.6 59.9 82.4 49.2 30.9 76.2 77.9 (bushels per ), a. (4pt) Find the Regression equation: = b. (2pt) Find the coefficient of determination: c. (2pt) Find the coefficient of correlation: d. (1pt) What is the predicted value for y given x = 16.1? e. (1pt) What is the predicted value for y given x = 6.2? f. (1pt) Find the standard error of estimate for the data: Page 1 of 5 Hypothesis Tests - (13 points each - See scoring criteria in Canvas) A study was conducted to determine if the salaries of elementary school teachers from two neighboring districts were equal. A sample of teachers from each district was randomly selected. Test the claim that the salaries from both districts are equal. Assume the samples are random, independent and populations are normally distributed. Also, assume that they have unequal variances. Use a = 0.04. (Round to four decimals) Ho: H: = Which hypothesis represents the claim? Circle: Null Hypothesis or Alternative Hypothesis Find the critical values of the rejection region. (Show calculator function used, values plugged into calculator function, and final answer rounded to 4 District 1 x = $39,800 S = $1073 District 2 n = 21 x = $26,800 S = $2290 n = 28 decimals. Sketch the rejection region on the normal curve.) Test this hypothesis. (Show original formula, values then plugged into formula, and final answer rounded to 4 decimals) Decision (Reject or Fail to Reject): Write a conclusion in context of this problem. At % level of significance, there, enough evidence to the claim that Page 2 of 5 A local brewery distributes beer in bottles labeled 30 ounces. A government agency thinks that the brewery is distributing less than that amount. The agency selects 40 of these bottles, measures their contents, and obtains a sample mean of 28.4 ounces with a population standard deviation of 1.1 ounce. Use a 0.03 significance level to test the agency's claim that the brewery is cheating its customers. (Round to four decimals) Ho H: a = Which hypothesis represents the claim? Circle: Null Hypothesis or Alternative Hypothesis Find the critical values of the rejection region. (Show calculator function used, values plugged into calculator function, and final answer rounded to 4 decimals. Sketch the rejection region on the normal curve.) Test this hypothesis. (Show original formula, values then plugged into formula, and final answer rounded to 4 decimals) Decision (Reject or Fail to Reject): Write a conclusion in context of this problem. At % level of significance, there enough evidence to the claim that Page 3 of 5 A telephone company claims that more than 18% of its customers have a home telephone line. The company selects a random sample of 400 customers and finds that 87 have home telephone lines. If a = 0.07, test the company's claim using critical values and rejection regions. (Round to four decimals) Ho: H: = Which hypothesis represents the claim? Circle: Null Hypothesis or Alternative Hypothesis Find the critical values of the rejection region. (Show calculator function used, values plugged into calculator function, and final answer rounded to 4 decimals. Sketch the rejection region on the normal curve.) Test the hypothesis. (Show original formula, values then plugged into formula, and final answer rounded to 4 decimals) Decision (Reject or Fail to Reject): Write a conclusion in context of this problem. At % level of significance, there enough evidence to the claim that Page 4 of 5 (2 points) BONUS: Correctly identify the prediction interval, rounded to 4 decimal places. Construct a 95% prediction interval for the price per gallon of milk when 160 billion pounds of milk is produced. The amounts of milk produced in the United States and the average prices (in dollars) per gallon of milk for nine years is given below. (Round to four decimal places). Milk produced, 157.6 163.5 170.1 170.4 170.9 177.0 194.8 185.7 195.0 x Price per 2.79 2.90 2.68 3.85 3.23 3.24 3.00 5.87 3.88 gallon, v to = Se = n = x0 = x= = x= = There is a 95% probability that the price per gallon (y) value is between based on 160 billion pounds of milk being produced. n(x-2) Etese 1+1 + n nx-x) Page 5 of 5